From 71053d55387266f33d9dfdf0b0984730f5a25f8c Mon Sep 17 00:00:00 2001 From: Daniel Bachar Date: Thu, 6 Jan 2022 15:35:16 -1000 Subject: [PATCH 1/2] CountMInSketch - Implementation + testing + readme --- .../CountMinSketch.playground/Contents.swift | 111 +++++++ .../contents.xcplayground | 4 + .../contents.xcworkspacedata | 7 + CountMinSketch/CountMinSketch.swift | 89 ++++++ CountMinSketch/Images/algorithm.png | Bin 0 -> 596826 bytes CountMinSketch/Images/matrix_def.png | Bin 0 -> 184947 bytes CountMinSketch/README.markdown | 27 ++ .../Tests/Tests.xcodeproj/project.pbxproj | 277 ++++++++++++++++++ .../contents.xcworkspacedata | 7 + .../xcshareddata/IDEWorkspaceChecks.plist | 8 + .../xcshareddata/xcschemes/Tests.xcscheme | 56 ++++ .../Tests/Tests/CountMinSketchTests.swift | 34 +++ CountMinSketch/Tests/Tests/Info.plist | 22 ++ 13 files changed, 642 insertions(+) create mode 100644 CountMinSketch/CountMinSketch.playground/Contents.swift create mode 100644 CountMinSketch/CountMinSketch.playground/contents.xcplayground create mode 100644 CountMinSketch/CountMinSketch.playground/playground.xcworkspace/contents.xcworkspacedata create mode 100644 CountMinSketch/CountMinSketch.swift create mode 100644 CountMinSketch/Images/algorithm.png create mode 100644 CountMinSketch/Images/matrix_def.png create mode 100644 CountMinSketch/README.markdown create mode 100644 CountMinSketch/Tests/Tests.xcodeproj/project.pbxproj create mode 100644 CountMinSketch/Tests/Tests.xcodeproj/project.xcworkspace/contents.xcworkspacedata create mode 100644 CountMinSketch/Tests/Tests.xcodeproj/project.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist create mode 100644 CountMinSketch/Tests/Tests.xcodeproj/xcshareddata/xcschemes/Tests.xcscheme create mode 100644 CountMinSketch/Tests/Tests/CountMinSketchTests.swift create mode 100644 CountMinSketch/Tests/Tests/Info.plist diff --git a/CountMinSketch/CountMinSketch.playground/Contents.swift b/CountMinSketch/CountMinSketch.playground/Contents.swift new file mode 100644 index 000000000..58f7e64f6 --- /dev/null +++ b/CountMinSketch/CountMinSketch.playground/Contents.swift @@ -0,0 +1,111 @@ +//: # CountMin Sketch +import Foundation + +/// Private wrapper around Hashing, allowing hash different Hashables and keep their value +private final class Hashing where T: Hashable { + private var map: [T: Int] = [:] + + func hash(_ value: T) -> Int { + if let hash = map[value] { + return hash + } + var hasher = Hasher() + hasher.combine(value) + let newValue = abs(hasher.finalize()) + map[value] = newValue + return newValue + } +} + +/* + A class for counting hashable items using the Count-min Sketch strategy. + It fulfills a similar purpose than `itertools.Counter`. + The Count-min Sketch is a randomized data structure that uses a constant + amount of memory and has constant insertion and lookup times at the cost + of an arbitrarily small overestimation of the counts. +*/ +public final class CountMinSketch where T: Hashable { + private var hashers: [Hashing] = [] + private var matrix: [[UInt64]] = [] + private let rows: Int + private let cols: Int + + /// The total amount of elements adedd to the model + private(set) var count: UInt64 = 0 + /// init - will determine the matrix size + /// - Parameters: + /// - rows: the size of the hash tables, larger implies smaller overestimation + /// - cols: the amount of hash tables, larger implies lower probability of + init(rows: Int, cols: Int) { + self.rows = rows + self.cols = cols + for _ in 0.. UInt64 { + var values = [UInt64]() + for row in 0..(rows: 10, cols: 10) + +for element in stream { + sketch.add(element: element) +} + +assert(sketch.count == stream.count) + +print("We have \(sketch.count) elements in the stream") + + +print("The frequency of 1 is \(sketch.query(element: 1))") diff --git a/CountMinSketch/CountMinSketch.playground/contents.xcplayground b/CountMinSketch/CountMinSketch.playground/contents.xcplayground new file mode 100644 index 000000000..fd676d5b4 --- /dev/null +++ b/CountMinSketch/CountMinSketch.playground/contents.xcplayground @@ -0,0 +1,4 @@ + + + + \ No newline at end of file diff --git a/CountMinSketch/CountMinSketch.playground/playground.xcworkspace/contents.xcworkspacedata b/CountMinSketch/CountMinSketch.playground/playground.xcworkspace/contents.xcworkspacedata new file mode 100644 index 000000000..919434a62 --- /dev/null +++ b/CountMinSketch/CountMinSketch.playground/playground.xcworkspace/contents.xcworkspacedata @@ -0,0 +1,7 @@ + + + + + diff --git a/CountMinSketch/CountMinSketch.swift b/CountMinSketch/CountMinSketch.swift new file mode 100644 index 000000000..b8e4ece55 --- /dev/null +++ b/CountMinSketch/CountMinSketch.swift @@ -0,0 +1,89 @@ +import Foundation + +/// Private wrapper around Hashing, allowing hash different Hashables and keep their value +private final class Hashing where T: Hashable { + private var map: [T: Int] = [:] + + func hash(_ value: T) -> Int { + if let hash = map[value] { + return hash + } + var hasher = Hasher() + hasher.combine(value) + let newValue = abs(hasher.finalize()) + map[value] = newValue + return newValue + } +} + +/* + A class for counting hashable items using the Count-min Sketch strategy. + It fulfills a similar purpose than `itertools.Counter`. + The Count-min Sketch is a randomized data structure that uses a constant + amount of memory and has constant insertion and lookup times at the cost + of an arbitrarily small overestimation of the counts. +*/ +public final class CountMinSketch where T: Hashable { + private var hashers: [Hashing] = [] + private var matrix: [[UInt64]] = [] + private let rows: Int + private let cols: Int + + /// The total amount of elements adedd to the model + private(set) var count: UInt64 = 0 + /// init - will determine the matrix size + /// - Parameters: + /// - rows: the size of the hash tables, larger implies smaller overestimation + /// - cols: the amount of hash tables, larger implies lower probability of + init(rows: Int, cols: Int) { + self.rows = rows + self.cols = cols + for _ in 0.. 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b/CountMinSketch/README.markdown new file mode 100644 index 000000000..ee4f3c93c --- /dev/null +++ b/CountMinSketch/README.markdown @@ -0,0 +1,27 @@ +# CountMin Sketch + +#### Explanation about the model (Taken from wikipedia) +In computing, the count–min sketch (CM sketch) is a probabilistic data structure that serves as a frequency table of events in a stream of data. It uses hash functions to map events to frequencies, but unlike a hash table uses only sub-linear space, at the expense of overcounting some events due to collisions. The count–min sketch was invented in 2003 by Graham Cormode and S. Muthu Muthukrishnan and described by them in a [2005 paper](https://www.sciencedirect.com/science/article/abs/pii/S0196677403001913?via%3Dihub). + +The goal of the basic version of the count–min sketch is to consume a stream of events, one at a time, and count the frequency of the different types of events in the stream. At any time, the sketch can be queried for the frequency of a particular event type i from a universe of event types {U}, and will return an estimate of this frequency that is within a certain distance of the true frequency, with a certain probability. + +The actual sketch data structure is a two-dimensional array of w columns and d rows. The parameters w and d are fixed when the sketch is created, and determine the time and space needs and the probability of error when the sketch is queried for a frequency or inner product. Associated with each of the d rows is a separate hash function; the hash functions must be pairwise independent. The parameters w and d can be chosen by setting w = ⌈2/ε⌉ and d = ⌈ln 1/δ⌉, where the error in answering a query is within an additive factor of ε with probability 1 − δ +When a new event of type i arrives we update as follows: for each row j of the table, apply the corresponding hash function to obtain a column index k = hj(i). Then increment the value in row j, column k by one. + +![algorithm](Images/algorithm.png "Algorithm and main Data Structure") +![matrix_def](Images/matrix_def.png "Matrix size and definitions") + + +#### Implementation details +1. Memory consumption - We hold a matrix in the size according to the probalictic charactaristic the user wish, specifically we will have cols = ⌈2/ε⌉ and row = ⌈ln 1/δ⌉ +2. `add` function - Given the assumption applying a hash function takes O(1) as well as arithmetic addition `adding` an element shall take O(⌈ln 1/δ⌉) = O(number of rows) +3. `query` - Same as adding - O(⌈ln 1/δ⌉) = O(number of rows) + + +#### How is this different from a regular counter +This model allows us to use sublinear space to estimate the frequecny of elements if a stream. +While a regualr counter will have to maintain some mapping between each element to its frequency, this model allows us to use probability and have a smaller memory footprint. +This value of this Data Structure makes it particulary benefitial for huge data streams where it is not feasable to hold an exact counter for each elements as the stream is potentially endless. + + +*Written by Daniel Bachar* diff --git a/CountMinSketch/Tests/Tests.xcodeproj/project.pbxproj b/CountMinSketch/Tests/Tests.xcodeproj/project.pbxproj new file mode 100644 index 000000000..19edde1d2 --- /dev/null +++ b/CountMinSketch/Tests/Tests.xcodeproj/project.pbxproj @@ -0,0 +1,277 @@ +// !$*UTF8*$! +{ + archiveVersion = 1; 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